gift-framework · gift-framework · Feb 22, 2026 · Feb 22, 2026 · Feb 22, 2026 · Feb 22, 2026
diff --git a/CHANGELOG.md b/CHANGELOG.md
@@ -5,6 +5,51 @@ All notable changes to GIFT Core will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
+## [3.3.23] - 2026-02-22
+
+### Summary
+
+**Certificate modularization: monolithic → domain-organized.** Restructures the 2281-line monolithic `Certificate.lean` (55 theorems, 233 abbrevs, 9 stacked master theorems) into four focused files organized by mathematical domain. Removes 16 versioned certificates and 9 stacked master theorems. The new structure uses `def statement : Prop` / `theorem certified : statement` pattern for composability. One master certificate combines all three pillars: `Foundations.statement ∧ Predictions.statement ∧ Spectral.statement`. Backward-compatible `Certificate.lean` wrapper preserves legacy aliases. Zero proof changes, full build passes (2651 jobs).
+
+### Added
+
+- **Certificate/Foundations.lean** (~440 lines) — E₈ root system, G₂ cross product, octonion bridge, K₇ Betti numbers, exterior algebra, Joyce existence, Sobolev embedding, conformal rigidity, Poincare duality, G₂ metric properties, TCS piecewise structure:
+  - 80+ abbrevs creating dependency graph edges
+  - `def statement : Prop` with 19 conjuncts
+  - `theorem certified : statement` proven via `refine` + `native_decide`
+
+- **Certificate/Predictions.lean** (~460 lines) — All 33+ published dimensionless predictions (R1-R20), V5.0 observables (~50 rational fractions), Fano selection principle, tau bounds, hierarchy, SO(16) decomposition, Landauer dark energy:
+  - 30+ abbrevs for Relations submodules
+  - `def statement : Prop` with 48 conjuncts
+  - 7 additional theorems: `observables_certified`, `the_42_universality`, `fano_selection_certified`, `tau_bounds_certified`, `hierarchy_certified`, `SO16_certified`, `landauer_certified`
+
+- **Certificate/Spectral.lean** (~380 lines) — Mass gap ratio 14/99, TCS manifold structure, TCS spectral bounds, selection principle, refined bounds, literature axioms, spectral scaling, Connes bridge:
+  - 60+ abbrevs for Spectral submodules
+  - `def statement : Prop` with 27 conjuncts
+  - `theorem certified : statement` proven via `repeat (first | constructor | native_decide | rfl | norm_num)`
+
+- **Certificate/Core.lean** (~40 lines) — Single master certificate:
+  - `theorem gift_master_certificate : Foundations.statement ∧ Predictions.statement ∧ Spectral.statement`
+
+### Changed
+
+- **Certificate.lean** — Replaced 2281-line monolithic file with ~35-line backward-compat wrapper:
+  - Imports `GIFT.Certificate.Core`
+  - Provides legacy aliases: `all_relations_certified`, `gift_v32_foundations_certificate`, `gift_v338_yang_mills_certificate`, `gift_v50_extended_observables_certificate`
+- **GIFT.lean** — Updated import from `GIFT.Certificate` to `GIFT.Certificate.Core`
+- **CLAUDE.md** — Updated project structure, certificate workflow documentation
+- **docs/USAGE.md** — Added v3.3.23 certificate modularization section
+- **blueprint/src/content.tex** — Updated Grand Certificate reference to `gift_master_certificate`
+
+### Removed
+
+- 9 stacked master theorems (`all_13_relations_certified` → `all_75_relations_certified`)
+- 16 versioned certificates (`gift_v2_*`, `gift_v3_*`, `gift_v32_*`, etc.)
+- Trivial certificates (`True := by trivial`)
+- ~1400 lines of redundant code
+
+---
+
 ## [3.3.22] - 2026-02-22
 
 ### Summary

diff --git a/CLAUDE.md b/CLAUDE.md
@@ -30,7 +30,12 @@ gift-framework/core/
 │   ├── GIFT.lean           # Main entry point
 │   ├── GIFT/
 │   │   ├── Core.lean       # Source of truth for constants
-│   │   ├── Certificate.lean # Master theorems (185+ relations)
+│   │   ├── Certificate/    # Modular certificate system (v3.3.23)
+│   │   │   ├── Core.lean       # Master: Foundations ∧ Predictions ∧ Spectral
+│   │   │   ├── Foundations.lean # E₈, G₂, octonions, K₇, Joyce
+│   │   │   ├── Predictions.lean # 33+ published relations, observables
+│   │   │   └── Spectral.lean   # Mass gap 14/99, TCS, selection
+│   │   ├── Certificate.lean # Backward-compat wrapper (legacy aliases)
 │   │   │
 │   │   ├── Algebra.lean    # E₈, G₂, E₇, F₄, E₆ constants
 │   │   ├── Topology.lean   # Betti numbers, H*, p₂
@@ -221,8 +226,11 @@ python -c "from gift_core import *; print(GAMMA_GIFT)"
 ## Adding New Certified Relations
 
 1. **Lean**: Create/update file in `Lean/GIFT/Relations/`
-2. **Lean**: Add import to `Lean/GIFT/Certificate.lean`
-3. **Lean**: Add to master theorem
+2. **Lean**: Add import + abbrev to appropriate `Certificate/` sub-module:
+   - `Certificate/Foundations.lean` — math infrastructure (E₈, G₂, K₇, Joyce)
+   - `Certificate/Predictions.lean` — physical predictions, observables
+   - `Certificate/Spectral.lean` — spectral gap, TCS, selection
+3. **Lean**: Add conjunct to the sub-module's `def statement : Prop`
 4. **Python**: Add constants to `gift_core/constants.py`
 5. **Python**: Export in `gift_core/__init__.py`
 6. **Python**: Add tests in `tests/`
@@ -598,31 +606,33 @@ theorem H_star_value : H_star = 99 := by unfold H_star b2 b3; norm_num  -- WORKS
 To connect an isolated module to the dependency graph:
 
 ```lean
--- In Certificate.lean:
+-- In the appropriate Certificate/ sub-module (e.g., Certificate/Foundations.lean):
 import GIFT.NewModule  -- Add import
 
 -- Create abbrevs for key theorems (creates edges)
 abbrev new_theorem := NewModule.key_theorem
 
--- Add to certification theorem
-theorem gift_certificate :
-    ...existing relations... ∧
+-- Add conjuncts to the sub-module's statement
+def statement : Prop :=
+    ...existing conjuncts... ∧
     -- Use VALUES directly, not theorem names
     (NewModule.some_value = 42) ∧
-    (NewModule.x + NewModule.y = NewModule.z) := by
+    (NewModule.x + NewModule.y = NewModule.z)
+
+theorem certified : statement := by
   repeat (first | constructor | native_decide | rfl)
 ```
 
 ### 9. Blueprint Dependency Graph Orphans
 
-**Problem**: Modules imported in Certificate.lean but without `abbrev` references appear as isolated clusters in the blueprint dependency graph.
+**Problem**: Modules imported in a `Certificate/` sub-module but without `abbrev` references appear as isolated clusters in the blueprint dependency graph.
 
 **Diagnosis**: Check the blueprint visualization. Disconnected clusters indicate missing `abbrev` edges.
 
-**Fix**: For each orphaned module, add abbrevs in Certificate.lean:
+**Fix**: For each orphaned module, add abbrevs in the appropriate `Certificate/` sub-module:
 
 ```lean
--- Module is imported but orphaned
+-- In Certificate/Foundations.lean (or Predictions.lean, Spectral.lean):
 import GIFT.SomeModule
 
 -- Fix: Add abbrevs to create dependency graph edges

diff --git a/Lean/GIFT.lean b/Lean/GIFT.lean
@@ -1,51 +1,57 @@
 -- GIFT: Geometric Integration of Fundamental Topologies
 -- Main entry point for Lean 4 formalization
--- Version: 3.3.17 (290+ certified relations + Physical Spectral Gap + Selberg Bridge)
+-- Version: 4.0.0 (290+ certified relations, modular certificate structure)
+
+-- ═══════════════════════════════════════════════════════════════════════════════
+-- CORE & RELATIONS
+-- ═══════════════════════════════════════════════════════════════════════════════
 
 import GIFT.Core
 import GIFT.Relations
-import GIFT.Certificate
-
--- V4.0: Mathematical Foundations (real content, not just arithmetic)
-import GIFT.Foundations
-
--- V5.0: Algebraic Foundations (octonion-based derivation)
-import GIFT.Algebraic
-
--- Topological Extension: +12 relations (25 total)
 import GIFT.Relations.GaugeSector
 import GIFT.Relations.NeutrinoSector
 import GIFT.Relations.LeptonSector
 import GIFT.Relations.Cosmology
-
--- Mass Factorization Theorem: +11 relations (v1.6.0)
 import GIFT.Relations.MassFactorization
 
--- V2.0 New modules
-import GIFT.Sequences      -- Fibonacci, Lucas, Recurrence
-import GIFT.Primes         -- Prime Atlas (direct, derived, Heegner)
-import GIFT.Moonshine      -- Monstrous moonshine (Monster group, j-invariant)
-import GIFT.McKay          -- McKay correspondence, Golden emergence
+-- ═══════════════════════════════════════════════════════════════════════════════
+-- MATHEMATICAL FOUNDATIONS
+-- ═══════════════════════════════════════════════════════════════════════════════
+
+import GIFT.Foundations
+import GIFT.Algebraic
+import GIFT.Geometry
+
+-- Joyce existence theorem
+import GIFT.Sobolev
+import GIFT.DifferentialForms
+import GIFT.ImplicitFunction
+import GIFT.IntervalArithmetic
+import GIFT.Joyce
 
--- V3.0: Joyce Perturbation Theorem
-import GIFT.Sobolev            -- Sobolev spaces H^k
-import GIFT.DifferentialForms  -- Exterior calculus
-import GIFT.ImplicitFunction   -- Implicit function theorem
-import GIFT.IntervalArithmetic -- Verified numerical bounds
-import GIFT.Joyce              -- Torsion-free G2 existence
+-- Dimensional hierarchy & golden ratio
+import GIFT.Foundations.GoldenRatioPowers
+import GIFT.Hierarchy
 
--- V4.0: Dimensional Hierarchy
-import GIFT.Foundations.GoldenRatioPowers  -- phi^-2, phi^-54, 27^phi
-import GIFT.Hierarchy                       -- Master hierarchy formula
+-- ═══════════════════════════════════════════════════════════════════════════════
+-- OBSERVABLES & SPECTRAL THEORY
+-- ═══════════════════════════════════════════════════════════════════════════════
 
--- V5.0: Extended Observables (~50 observables, 0.24% mean deviation)
-import GIFT.Observables  -- PMNS, CKM, mass ratios, cosmology
+import GIFT.Observables
+import GIFT.Spectral
 
--- V3.3.3: DG-Ready Geometry Infrastructure
-import GIFT.Geometry  -- Exterior algebra, differential forms, Hodge star on ℝ⁷
+-- ═══════════════════════════════════════════════════════════════════════════════
+-- EXTENSIONS (standalone modules, compiled but not in Certificate)
+-- ═══════════════════════════════════════════════════════════════════════════════
+
+import GIFT.Sequences      -- Fibonacci, Lucas, Recurrence
+import GIFT.Primes         -- Prime Atlas (direct, derived, Heegner)
+import GIFT.Moonshine      -- Monstrous moonshine (Monster group, j-invariant)
+import GIFT.McKay          -- McKay correspondence, Golden emergence
+import GIFT.MollifiedSum   -- Cosine-squared kernel, mollified sum S_w(T)
 
--- V3.3.8: Spectral Gap (Yang-Mills mass gap)
-import GIFT.Spectral  -- Mass gap ratio, Cheeger bounds, Yang-Mills prediction
+-- ═══════════════════════════════════════════════════════════════════════════════
+-- CERTIFICATE (modular: Foundations / Predictions / Spectral)
+-- ═══════════════════════════════════════════════════════════════════════════════
 
--- V3.3.16: Mollified Dirichlet Polynomial + Selberg Bridge
-import GIFT.MollifiedSum  -- Cosine-squared kernel, mollified sum S_w(T)
+import GIFT.Certificate.Core